Question

Let f left-parenthesis x right-parenthesis equals 2 x squared plus x minus 3 and g left-parenthesis x right-parenthesis equals x minus 1. Perform the indicated operation, then find the domain.StartFraction f over g EndFraction left-parenthesis x right-parenthesisA) 1 over 2 x plus 3 EndFraction; domain: all real numbers except x equals negative three-halvesB) 2x + 3; domain: all real numbersC) 2 x squared plus 3; domain: all real numbersD) 2x + 3; domain: all real numbers except x = 1

Answer 1

F(x)= 2x^2 +x - 3

g(x)= x-1

f/g (x) =

$\frac{f}{g}(x)=\frac{2x^2+x-3}{x-1}$

Factor by grouping:

$\frac{f}{g}(x)=\frac{(x-1)(2x+3)}{(x-1)}$

$\frac{f}{g}(x)=2x+3$

Domain= all real numbers.

B) 2x + 3; domain: all real numbers